Subtract and Conquer

Duration: 2 min

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Module outline

  1. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  2. DataBase Management System/DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  6. C Language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  10. Theory Of Computation/Automata Theory: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  11. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  12. Engineering Mathematics: Permutation and Combination, Linear Algebra, Calculus, Probability, Statistics
  13. General Aptitude: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Mensuration and Geometry, Mental Ability, Arithmetic, Profit and Loss, Powers and Exponents (Surds and Indices), Average, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, Venn Diagram, Seating Arrangements, Blood Relations, Directions (Direction Test), Analogy, Algebra, Time and Work, Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Cubes & Dices, Ranking, Order and Sequence, Mixture and Alligation, Age Problems, Clock, Selection Decision Table (Decision Making), Data Arrangement
  14. English (Verbal Aptitude): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Direct and Indirect Speech, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Verbal Analogy (Word Based Analogy), Conjunction, Interjection, Verb, Articles, Adverb, Modals, Sentence Construction
  15. Live Classes Recordings(Earlier Batch): GATE 2026 Live Class
  16. Full Mock Test:
  17. Previous Year Papers:
  18. GATE 2026 Counselling: Counselling and Guidance Sessions
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video focuses on analyzing the time complexity of a specific recurrence relation commonly found in divide-and-conquer algorithms. The instructor presents the inequality T(n) <= c if n <= 1, and aT(n-b) + f(n) if n > 1. He explains that a represents the number of subproblems, b is the reduction in problem size, and f(n) is the cost of dividing and combining. The core of the lesson involves determining the Big-O complexity of T(n) given that f(n) is O(n^k). The instructor systematically breaks down the solution into three distinct scenarios based on the value of a.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by writing the recurrence relation on the screen. He then draws a rough tree diagram to illustrate the recursive structure, labeling the root as T(n) and the branches as T(n-b). He explicitly writes the condition 'If f(n) is O(n^k)' to set the context for the complexity analysis. Following this, he lists three numbered cases on the left side of the screen. Case 1 states that if a < 1, then T(n) = O(n^k). Case 2 states that if a = 1, then T(n) = O(n^{k+1}). Case 3 states that if a > 1, then T(n) = O(n^k a^{n/b}). As he discusses each case, he draws a blue checkmark next to it to indicate validity or completion of the point. He also circles the assumption f(n) = O(n^k) to emphasize its importance.

  2. 2:00 – 2:04 02:00-02:04

    The video ends with the instructor having completed the list of cases. The screen displays the full recurrence relation at the top and the three solved cases at the bottom, providing a complete reference for this specific type of recurrence.

The lecture provides a concise summary of the solution for a linear recurrence relation where the problem size decreases by a constant b at each step. It categorizes the complexity based on whether the number of subproblems (a) is less than, equal to, or greater than 1, assuming the non-recursive work is polynomial.

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